Log-Linear DRiT - MA Data Analysis

Scatter plot

Food waste plots

Log-Linear RDiT Model

Interaction

## 
## Call:
## lm(formula = rdt_int_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.07089 -0.29053  0.07099  0.31294  0.92461 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.899186   0.100117   8.981  7.9e-16 ***
## container       0.125174   0.145241   0.862   0.3901    
## time           -0.003624   0.001999  -1.813   0.0717 .  
## container:time  0.004636   0.003166   1.464   0.1451    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4602 on 157 degrees of freedom
## Multiple R-squared:  0.02157,    Adjusted R-squared:  0.002876 
## F-statistic: 1.154 on 3 and 157 DF,  p-value: 0.3293
## 
## Call:
## lm(formula = rdt_int_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49626 -0.17125 -0.02458  0.17911  0.84798 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.456958   0.058104   7.864 5.59e-13 ***
## container      -0.002367   0.084292  -0.028    0.978    
## time           -0.001638   0.001160  -1.412    0.160    
## container:time  0.001864   0.001837   1.015    0.312    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2671 on 157 degrees of freedom
## Multiple R-squared:  0.0273, Adjusted R-squared:  0.008717 
## F-statistic: 1.469 on 3 and 157 DF,  p-value: 0.2251
## 
## Call:
## lm(formula = rdt_int_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.86306 -0.32547  0.08476  0.29523  0.83820 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.647578   0.089499   7.236 1.93e-11 ***
## container       0.172827   0.129837   1.331   0.1851    
## time           -0.003520   0.001787  -1.970   0.0506 .  
## container:time  0.004447   0.002830   1.572   0.1181    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4114 on 157 degrees of freedom
## Multiple R-squared:  0.02936,    Adjusted R-squared:  0.01082 
## F-statistic: 1.583 on 3 and 157 DF,  p-value: 0.1956

Ass-Interaction

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.654).
## OK: Error variance appears to be homoscedastic (p = 0.064).
## OK: Error variance appears to be homoscedastic (p = 0.778).
## Warning: Non-normality of residuals detected (p = 0.014).
## Warning: Non-normality of residuals detected (p = 0.044).
## Warning: Non-normality of residuals detected (p = 0.004).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_fw_log
## BP = 1.4669, df = 3, p-value = 0.6899
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_sfw_log
## BP = 3.892, df = 3, p-value = 0.2734
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_lfw_log
## BP = 2.2738, df = 3, p-value = 0.5176
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: Residuals appear to be independent and not autocorrelated (p = 0.696).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.680).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.598).

Multiple model

## 
## Call:
## lm(formula = rdt_multi_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.70381 -0.21143 -0.01368  0.21472  0.89566 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.2025206  0.3094972  -0.654  0.51391    
## container       0.1371993  0.1171206   1.171  0.24333    
## time           -0.0009055  0.0021069  -0.430  0.66799    
## temp_c         -0.0003912  0.0040574  -0.096  0.92332    
## humi_p          0.0021214  0.0029957   0.708  0.47999    
## prcp_mm        -0.0197288  0.0129534  -1.523  0.12991    
## tueE            0.0791179  0.0604806   1.308  0.19288    
## wedE           -0.0539749  0.0600338  -0.899  0.37009    
## thuE           -0.0914458  0.0582575  -1.570  0.11865    
## friE            0.0253774  0.0570715   0.445  0.65722    
## satE           -0.0820893  0.0599080  -1.370  0.17271    
## liquors         0.0099865  0.0170719   0.585  0.55947    
## sales           0.0012110  0.0001851   6.544  9.5e-10 ***
## halfs           0.0311432  0.0093690   3.324  0.00112 ** 
## container:time  0.0011543  0.0032081   0.360  0.71952    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.32 on 146 degrees of freedom
## Multiple R-squared:   0.56,  Adjusted R-squared:  0.5179 
## F-statistic: 13.27 on 14 and 146 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_multi_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41365 -0.15187 -0.03471  0.12691  0.87801 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.0830067  0.2039018  -0.407   0.6845    
## container       0.0312116  0.0771610   0.405   0.6864    
## time           -0.0002954  0.0013880  -0.213   0.8318    
## temp_c         -0.0011196  0.0026731  -0.419   0.6759    
## humi_p          0.0002079  0.0019736   0.105   0.9163    
## prcp_mm        -0.0109674  0.0085339  -1.285   0.2008    
## tueE            0.0817078  0.0398456   2.051   0.0421 *  
## wedE           -0.0098532  0.0395513  -0.249   0.8036    
## thuE           -0.0723120  0.0383810  -1.884   0.0615 .  
## friE            0.0170265  0.0375997   0.453   0.6513    
## satE           -0.0516432  0.0394684  -1.308   0.1928    
## liquors         0.0066501  0.0112472   0.591   0.5553    
## sales           0.0007099  0.0001219   5.823 3.54e-08 ***
## halfs           0.0096277  0.0061724   1.560   0.1210    
## container:time -0.0003659  0.0021136  -0.173   0.8628    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2108 on 146 degrees of freedom
## Multiple R-squared:  0.4364, Adjusted R-squared:  0.3823 
## F-statistic: 8.074 on 14 and 146 DF,  p-value: 1.421e-12
## 
## Call:
## lm(formula = rdt_multi_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.64161 -0.19503  0.00511  0.19954  0.72644 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.3398374  0.2771014  -1.226 0.222022    
## container       0.1723560  0.1048614   1.644 0.102399    
## time           -0.0012647  0.0018863  -0.670 0.503613    
## temp_c         -0.0002052  0.0036327  -0.056 0.955037    
## humi_p          0.0023787  0.0026821   0.887 0.376597    
## prcp_mm        -0.0154073  0.0115976  -1.328 0.186087    
## tueE            0.0226180  0.0541500   0.418 0.676785    
## wedE           -0.0570734  0.0537500  -1.062 0.290065    
## thuE           -0.0728029  0.0521596  -1.396 0.164902    
## friE            0.0353672  0.0510977   0.692 0.489944    
## satE           -0.0588896  0.0536373  -1.098 0.274045    
## liquors         0.0066489  0.0152849   0.435 0.664208    
## sales           0.0010125  0.0001657   6.111 8.56e-09 ***
## halfs           0.0305461  0.0083883   3.642 0.000376 ***
## container:time  0.0018389  0.0028723   0.640 0.523038    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2865 on 146 degrees of freedom
## Multiple R-squared:  0.5622, Adjusted R-squared:  0.5202 
## F-statistic: 13.39 on 14 and 146 DF,  p-value: < 2.2e-16

Ass-Multiple

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.019).
## OK: Error variance appears to be homoscedastic (p = 0.448).
## OK: Error variance appears to be homoscedastic (p = 0.205).
## OK: residuals appear as normally distributed (p = 0.831).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.695).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_fw_log
## BP = 20.433, df = 14, p-value = 0.1171
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_sfw_log
## BP = 12.468, df = 14, p-value = 0.5688
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_lfw_log
## BP = 12.443, df = 14, p-value = 0.5708
## OK: Residuals appear to be independent and not autocorrelated (p = 0.674).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.602).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.616).

Quadratic model

## 
## Call:
## lm(formula = rdt_poly_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69414 -0.21485 -0.01643  0.20846  0.86740 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.143e-01  3.323e-01  -0.946  0.34584    
## container            1.217e-01  1.661e-01   0.732  0.46514    
## time                -5.608e-03  5.959e-03  -0.941  0.34821    
## I(time^2)           -5.680e-05  6.445e-05  -0.881  0.37959    
## tueE                 8.403e-02  6.077e-02   1.383  0.16885    
## wedE                -5.148e-02  6.017e-02  -0.855  0.39370    
## thuE                -8.756e-02  5.843e-02  -1.498  0.13619    
## friE                 2.777e-02  5.720e-02   0.485  0.62812    
## satE                -8.818e-02  6.018e-02  -1.465  0.14505    
## temp_c               1.016e-04  4.091e-03   0.025  0.98023    
## humi_p               2.575e-03  3.028e-03   0.850  0.39655    
## prcp_mm             -2.309e-02  1.325e-02  -1.742  0.08362 .  
## liquors              1.115e-02  1.712e-02   0.651  0.51593    
## sales                1.236e-03  1.864e-04   6.633  6.2e-10 ***
## halfs                3.051e-02  9.438e-03   3.232  0.00152 ** 
## container:time       1.241e-02  9.400e-03   1.320  0.18895    
## container:I(time^2) -3.033e-05  1.103e-04  -0.275  0.78368    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3204 on 144 degrees of freedom
## Multiple R-squared:  0.5649, Adjusted R-squared:  0.5166 
## F-statistic: 11.69 on 16 and 144 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_poly_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37382 -0.14580 -0.02945  0.12595  0.83578 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -2.350e-01  2.169e-01  -1.084   0.2803    
## container            7.135e-02  1.084e-01   0.658   0.5115    
## time                -7.037e-03  3.889e-03  -1.810   0.0724 .  
## I(time^2)           -7.958e-05  4.206e-05  -1.892   0.0605 .  
## tueE                 8.512e-02  3.966e-02   2.146   0.0335 *  
## wedE                -8.221e-03  3.927e-02  -0.209   0.8345    
## thuE                -6.772e-02  3.813e-02  -1.776   0.0778 .  
## friE                 2.029e-02  3.733e-02   0.544   0.5875    
## satE                -5.734e-02  3.927e-02  -1.460   0.1465    
## temp_c              -7.590e-04  2.670e-03  -0.284   0.7766    
## humi_p               7.689e-04  1.976e-03   0.389   0.6978    
## prcp_mm             -1.403e-02  8.650e-03  -1.622   0.1071    
## liquors              7.994e-03  1.117e-02   0.715   0.4755    
## sales                7.370e-04  1.216e-04   6.060 1.13e-08 ***
## halfs                8.552e-03  6.159e-03   1.389   0.1671    
## container:time       1.087e-02  6.134e-03   1.773   0.0784 .  
## container:I(time^2)  2.076e-05  7.197e-05   0.288   0.7734    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2091 on 144 degrees of freedom
## Multiple R-squared:  0.4532, Adjusted R-squared:  0.3924 
## F-statistic: 7.458 on 16 and 144 DF,  p-value: 1.713e-12
## 
## Call:
## lm(formula = rdt_poly_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63819 -0.19662  0.00115  0.19553  0.73005 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.425e-01  2.983e-01  -1.148 0.252852    
## container            9.485e-02  1.491e-01   0.636 0.525707    
## time                -9.383e-04  5.349e-03  -0.175 0.860998    
## I(time^2)            1.604e-06  5.785e-05   0.028 0.977924    
## tueE                 2.685e-02  5.455e-02   0.492 0.623250    
## wedE                -5.479e-02  5.401e-02  -1.014 0.312064    
## thuE                -7.183e-02  5.245e-02  -1.370 0.172951    
## friE                 3.540e-02  5.135e-02   0.689 0.491645    
## satE                -6.229e-02  5.402e-02  -1.153 0.250828    
## temp_c               1.960e-04  3.672e-03   0.053 0.957513    
## humi_p               2.460e-03  2.718e-03   0.905 0.367005    
## prcp_mm             -1.739e-02  1.190e-02  -1.462 0.145983    
## liquors              6.977e-03  1.537e-02   0.454 0.650533    
## sales                1.022e-03  1.673e-04   6.110 8.85e-09 ***
## halfs                3.079e-02  8.471e-03   3.635 0.000386 ***
## container:time       7.218e-03  8.438e-03   0.855 0.393773    
## container:I(time^2) -7.877e-05  9.900e-05  -0.796 0.427521    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2876 on 144 degrees of freedom
## Multiple R-squared:  0.5649, Adjusted R-squared:  0.5165 
## F-statistic: 11.68 on 16 and 144 DF,  p-value: < 2.2e-16

Ass-Poly

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.013).
## OK: Error variance appears to be homoscedastic (p = 0.434).
## OK: Error variance appears to be homoscedastic (p = 0.117).
## OK: residuals appear as normally distributed (p = 0.890).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.613).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_fw_log
## BP = 24.13, df = 16, p-value = 0.08671
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_sfw_log
## BP = 13.961, df = 16, p-value = 0.6016
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_lfw_log
## BP = 17.492, df = 16, p-value = 0.3545
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## OK: Residuals appear to be independent and not autocorrelated (p = 0.676).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.764).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.530).
## Warning in adf.test(df$log_food_waste_kg): p-value smaller than printed p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_food_waste_kg
## Dickey-Fuller = -5.7678, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## Warning in adf.test(df$log_solid_waste_kg): p-value smaller than printed
## p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_solid_waste_kg
## Dickey-Fuller = -6.8741, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## Warning in adf.test(df$log_liquid_waste_kg): p-value smaller than printed
## p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_liquid_waste_kg
## Dickey-Fuller = -5.0025, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary

Log-linear Cubic multiple model

## 
## Call:
## lm(formula = log_fw_rdt_mult_cubic, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.70638 -0.21978 -0.00819  0.20085  0.88926 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.467e-01  3.277e-01  -0.753  0.45276    
## D_01         1.535e-02  1.525e-01   0.101  0.91998    
## t_01        -4.504e-03  4.975e-03  -0.905  0.36682    
## temp_c       1.412e-03  4.104e-03   0.344  0.73126    
## humi_p       2.553e-03  3.038e-03   0.840  0.40202    
## prcp_mm     -2.443e-02  1.326e-02  -1.843  0.06744 .  
## liquors      9.864e-03  1.713e-02   0.576  0.56572    
## sales        1.232e-03  1.866e-04   6.599 7.37e-10 ***
## halfs        3.099e-02  9.482e-03   3.268  0.00136 ** 
## tueE         8.730e-02  6.082e-02   1.435  0.15337    
## wedE        -5.102e-02  6.036e-02  -0.845  0.39932    
## thuE        -8.900e-02  5.851e-02  -1.521  0.13045    
## friE         2.497e-02  5.726e-02   0.436  0.66345    
## satE        -8.816e-02  6.030e-02  -1.462  0.14590    
## I(t_01^2)   -8.219e-05  5.992e-05  -1.372  0.17231    
## I(t_01^3)   -3.608e-07  4.630e-07  -0.779  0.43714    
## D_01:t_01    1.323e-02  9.671e-03   1.368  0.17341    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.321 on 144 degrees of freedom
## Multiple R-squared:  0.5633, Adjusted R-squared:  0.5148 
## F-statistic: 11.61 on 16 and 144 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = log_sfw_rdt_mult_cubic, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36678 -0.14222 -0.03583  0.12732  0.84012 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.137e-01  2.136e-01  -1.001   0.3187    
## D_01         4.104e-02  9.941e-02   0.413   0.6804    
## t_01        -6.172e-03  3.243e-03  -1.903   0.0591 .  
## temp_c      -5.309e-04  2.676e-03  -0.198   0.8430    
## humi_p       7.627e-04  1.980e-03   0.385   0.7007    
## prcp_mm     -1.441e-02  8.644e-03  -1.667   0.0977 .  
## liquors      7.730e-03  1.117e-02   0.692   0.4900    
## sales        7.348e-04  1.217e-04   6.040 1.25e-08 ***
## halfs        8.612e-03  6.182e-03   1.393   0.1657    
## tueE         8.676e-02  3.965e-02   2.188   0.0303 *  
## wedE        -8.591e-03  3.935e-02  -0.218   0.8275    
## thuE        -6.834e-02  3.814e-02  -1.792   0.0753 .  
## friE         1.950e-02  3.733e-02   0.522   0.6023    
## satE        -5.739e-02  3.931e-02  -1.460   0.1464    
## I(t_01^2)   -7.031e-05  3.906e-05  -1.800   0.0740 .  
## I(t_01^3)    1.553e-08  3.018e-07   0.051   0.9590    
## D_01:t_01    1.085e-02  6.305e-03   1.721   0.0874 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2093 on 144 degrees of freedom
## Multiple R-squared:  0.4522, Adjusted R-squared:  0.3914 
## F-statistic:  7.43 on 16 and 144 DF,  p-value: 1.909e-12
## 
## Call:
## lm(formula = log_lfw_rdt_mult_cubic, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.65347 -0.20142 -0.00552  0.20877  0.72859 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.789e-01  2.943e-01  -0.948 0.344767    
## D_01        -2.936e-03  1.369e-01  -0.021 0.982922    
## t_01        -7.497e-04  4.467e-03  -0.168 0.866959    
## temp_c       1.665e-03  3.685e-03   0.452 0.652120    
## humi_p       2.430e-03  2.728e-03   0.891 0.374577    
## prcp_mm     -1.875e-02  1.191e-02  -1.575 0.117517    
## liquors      5.553e-03  1.538e-02   0.361 0.718659    
## sales        1.018e-03  1.676e-04   6.076 1.05e-08 ***
## halfs        3.131e-02  8.514e-03   3.677 0.000333 ***
## tueE         2.976e-02  5.461e-02   0.545 0.586718    
## wedE        -5.411e-02  5.419e-02  -0.998 0.319756    
## thuE        -7.313e-02  5.254e-02  -1.392 0.166094    
## friE         3.257e-02  5.142e-02   0.633 0.527484    
## satE        -6.215e-02  5.414e-02  -1.148 0.252934    
## I(t_01^2)   -4.927e-05  5.380e-05  -0.916 0.361372    
## I(t_01^3)   -5.401e-07  4.157e-07  -1.299 0.195981    
## D_01:t_01    8.200e-03  8.684e-03   0.944 0.346592    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2882 on 144 degrees of freedom
## Multiple R-squared:  0.5629, Adjusted R-squared:  0.5144 
## F-statistic: 11.59 on 16 and 144 DF,  p-value: < 2.2e-16

Ass-Poly

  1. Independence of the observations
  2. Normality of the residuals
  3. No influential points (outliers)
  4. Homoscedasticity of the residuals
  5. Linearity of the relationships between the dependent and independent variables
  6. No multicollinearity
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Warning in adf.test(df$log_food_waste_kg): p-value smaller than printed p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_food_waste_kg
## Dickey-Fuller = -5.7678, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## Warning in adf.test(df$log_solid_waste_kg): p-value smaller than printed
## p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_solid_waste_kg
## Dickey-Fuller = -6.8741, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## Warning in adf.test(df$log_liquid_waste_kg): p-value smaller than printed
## p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  df$log_liquid_waste_kg
## Dickey-Fuller = -5.0025, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
## OK: Residuals appear to be independent and not autocorrelated (p = 0.650).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.668).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.550).
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01991081      2.001594    0.68
##  Alternative hypothesis: rho != 0
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.04642712      2.014825   0.748
##  Alternative hypothesis: rho != 0
##  lag Autocorrelation D-W Statistic p-value
##    1    -0.002456668      1.981727   0.586
##  Alternative hypothesis: rho != 0
## 
##  Durbin-Watson test
## 
## data:  log_rdt_mult_cubic_of$`log food waste`
## DW = 2.0016, p-value = 0.3299
## alternative hypothesis: true autocorrelation is greater than 0
## 
##  Durbin-Watson test
## 
## data:  log_rdt_mult_cubic_of$`log solid waste`
## DW = 2.0148, p-value = 0.3605
## alternative hypothesis: true autocorrelation is greater than 0
## 
##  Durbin-Watson test
## 
## data:  log_rdt_mult_cubic_of$`log liquid waste`
## DW = 1.9817, p-value = 0.286
## alternative hypothesis: true autocorrelation is greater than 0
## OK: residuals appear as normally distributed (p = 0.870).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.612).
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## 
##  studentized Breusch-Pagan test
## 
## data:  log_rdt_mult_cubic_of$`log food waste`
## BP = 23.182, df = 16, p-value = 0.1089
## 
##  studentized Breusch-Pagan test
## 
## data:  log_rdt_mult_cubic_of$`log solid waste`
## BP = 14.093, df = 16, p-value = 0.5918
## 
##  studentized Breusch-Pagan test
## 
## data:  log_rdt_mult_cubic_of$`log liquid waste`
## BP = 15.567, df = 16, p-value = 0.4836
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.009).
## OK: Error variance appears to be homoscedastic (p = 0.458).
## OK: Error variance appears to be homoscedastic (p = 0.089).
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##  Term  VIF     VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  wedE 1.83 [ 1.54,  2.29]         1.35      0.55     [0.44, 0.65]
##  thuE 1.66 [ 1.41,  2.06]         1.29      0.60     [0.48, 0.71]
##  friE 1.65 [ 1.40,  2.05]         1.29      0.61     [0.49, 0.71]
##  satE 1.80 [ 1.51,  2.24]         1.34      0.56     [0.45, 0.66]
## 
## High Correlation
## 
##       Term   VIF     VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  I(t_01^2) 22.68 [17.42, 29.63]         4.76      0.04     [0.03, 0.06]
##  I(t_01^3) 14.04 [10.83, 18.29]         3.75      0.07     [0.05, 0.09]
## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif
## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif
## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif

Local log-linear Regression

Interaction - b/w week and month

## Loading required package: sandwich
## Warning: package 'sandwich' was built under R version 4.2.3
## Loading required package: AER
## Loading required package: survival
## Loading required package: Formula
## [1] 6.03181
## [1] 4.095261
## [1] 5.845282

Covariates continuity test

Placebo test

Donut hole test

Food waste

Solid Food waste

Liquid food waste

log-linear Multiple - month

## 
## Call:
## lm(formula = log_food_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51357 -0.16849  0.01946  0.12329  0.61325 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     0.2988962  0.6895540   0.433  0.66726   
## container       0.0751821  0.1844288   0.408  0.68595   
## time           -0.0035192  0.0090010  -0.391  0.69812   
## temp_c          0.0069893  0.0076565   0.913  0.36739   
## humi_p         -0.0036874  0.0071753  -0.514  0.61047   
## prcp_mm        -0.0482459  0.0274499  -1.758  0.08732 . 
## tueE            0.1637430  0.1050361   1.559  0.12776   
## wedE            0.0131842  0.1098702   0.120  0.90515   
## thuE           -0.0631627  0.0994321  -0.635  0.52929   
## friE            0.0006048  0.0987478   0.006  0.99515   
## satE           -0.1848926  0.1050318  -1.760  0.08684 . 
## liquors         0.0040398  0.0296279   0.136  0.89230   
## sales           0.0012807  0.0003682   3.478  0.00134 **
## halfs           0.0303484  0.0196676   1.543  0.13156   
## container:time  0.0092436  0.0137591   0.672  0.50599   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3018 on 36 degrees of freedom
## Multiple R-squared:  0.6852, Adjusted R-squared:  0.5627 
## F-statistic: 5.596 on 14 and 36 DF,  p-value: 1.496e-05
## 
## Call:
## lm(formula = log_solid_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23587 -0.09713 -0.00118  0.07621  0.37761 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.2503976  0.3792951   0.660 0.513350    
## container       0.0017171  0.1014466   0.017 0.986589    
## time           -0.0009035  0.0049511  -0.182 0.856225    
## temp_c          0.0076969  0.0042115   1.828 0.075913 .  
## humi_p         -0.0035071  0.0039469  -0.889 0.380123    
## prcp_mm        -0.0125956  0.0150991  -0.834 0.409673    
## tueE            0.0361610  0.0577760   0.626 0.535340    
## wedE            0.0311853  0.0604350   0.516 0.609000    
## thuE           -0.0499517  0.0546935  -0.913 0.367160    
## friE            0.0180888  0.0543171   0.333 0.741050    
## satE           -0.0788150  0.0577736  -1.364 0.180972    
## liquors         0.0058179  0.0162971   0.357 0.723185    
## sales           0.0007934  0.0002025   3.918 0.000383 ***
## halfs           0.0044730  0.0108184   0.413 0.681720    
## container:time  0.0012049  0.0075683   0.159 0.874395    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.166 on 36 degrees of freedom
## Multiple R-squared:  0.6558, Adjusted R-squared:  0.5219 
## F-statistic: 4.899 on 14 and 36 DF,  p-value: 5.863e-05
## 
## Call:
## lm(formula = log_liquid_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52081 -0.14938  0.01322  0.14151  0.59771 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    -0.0146367  0.6279620  -0.023  0.98153   
## container       0.0843277  0.1679554   0.502  0.61867   
## time           -0.0031940  0.0081970  -0.390  0.69909   
## temp_c          0.0024800  0.0069726   0.356  0.72416   
## humi_p         -0.0006411  0.0065344  -0.098  0.92239   
## prcp_mm        -0.0486593  0.0249981  -1.947  0.05943 . 
## tueE            0.1400310  0.0956541   1.464  0.15189   
## wedE           -0.0282689  0.1000564  -0.283  0.77916   
## thuE           -0.0598792  0.0905507  -0.661  0.51264   
## friE            0.0087874  0.0899275   0.098  0.92270   
## satE           -0.1478034  0.0956502  -1.545  0.13103   
## liquors         0.0050597  0.0269815   0.188  0.85230   
## sales           0.0009589  0.0003353   2.860  0.00701 **
## halfs           0.0333015  0.0179109   1.859  0.07118 . 
## container:time  0.0099003  0.0125301   0.790  0.43463   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2749 on 36 degrees of freedom
## Multiple R-squared:  0.6655, Adjusted R-squared:  0.5354 
## F-statistic: 5.116 on 14 and 36 DF,  p-value: 3.793e-05

log-linear Multi - b/w week and month

Quadratic - b/w week and month

Cubic - b/w week and month